Abstract

We introduce a method for measuring the anisotropy of nonlinear absorption and nonlinear refraction in crystals by incorporating a wave plate into the Z-scan apparatus. We demonstrate this method by measuring the polarization dependence of the nonlinear refractive index or two-photon absorption coefficient in BaF2, KTP, and GaAs at wavelengths of 532 and 1064 nm.

© 1993 Optical Society of America

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  1. E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
    [CrossRef]
  2. R. Adair, L. L. Chase, S. A. Payne, Phys. Rev. B 39, 3337 (1989).
    [CrossRef]
  3. A. Owyoung, IEEE J. Quantum Electron. QE-11, 1064 (1973).
    [CrossRef]
  4. P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
    [CrossRef]
  5. Y. Bae, J. J. Song, Y. B. Kim, J. Appl. Phys. 53, 615 (1982).
    [CrossRef]
  6. A. A. Borshch, M. S. Brodin, V. N. Semioshko, Phys. Status Solidi A 91, 135 (1985).
    [CrossRef]
  7. W. E. Williams, M. J. Soileau, E. W. Van Stryland, in Fifteenth Annual Symposium on Optical Materials for High Power Lasers (National Bureau of Standards, Washington, D.C., 1983).
  8. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron 26, 760 (1990).
    [CrossRef]
  9. S. J. Bepko, Phys. Rev. B 12, 669 (1975).
    [CrossRef]
  10. J. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, E. W. Van Stryland, in Optical Society of America Annual Meeting Technical Digest (Optical Society of America, Washington, D.C., 1990), paper MTT7.
  11. S. I. Shablaev, Sov. Phys. JETP 70, 1105 (1990).
  12. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
    [CrossRef]
  13. P. N. Butcher, D. Cotter, Elements of Nonlinear Optics (Cambridge U. Press, London, 1990), Chap. 2.
    [CrossRef]
  14. D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
    [CrossRef]
  15. T. Yee Fan, C. E. Huang, B. Q. Hu, R. C. Echardt, Y. X. Fan, R. L. Byer, R. S. Feigelson, Appl. Opt. 26, 2390 (1987).
    [CrossRef]
  16. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17, 28 (1992).
    [CrossRef] [PubMed]
  17. C. Flytzanis, Phys. Lett. 31A, 273 (1970).
  18. E. Yablonovitch, C. Flytzanis, N. Bloembergen, Phys. Rev. Lett. 29, 865 (1972).
    [CrossRef]

1992 (3)

1991 (1)

E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

1990 (2)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron 26, 760 (1990).
[CrossRef]

S. I. Shablaev, Sov. Phys. JETP 70, 1105 (1990).

1989 (1)

R. Adair, L. L. Chase, S. A. Payne, Phys. Rev. B 39, 3337 (1989).
[CrossRef]

1987 (1)

1985 (1)

A. A. Borshch, M. S. Brodin, V. N. Semioshko, Phys. Status Solidi A 91, 135 (1985).
[CrossRef]

1982 (1)

Y. Bae, J. J. Song, Y. B. Kim, J. Appl. Phys. 53, 615 (1982).
[CrossRef]

1975 (1)

S. J. Bepko, Phys. Rev. B 12, 669 (1975).
[CrossRef]

1973 (1)

A. Owyoung, IEEE J. Quantum Electron. QE-11, 1064 (1973).
[CrossRef]

1972 (1)

E. Yablonovitch, C. Flytzanis, N. Bloembergen, Phys. Rev. Lett. 29, 865 (1972).
[CrossRef]

1970 (1)

C. Flytzanis, Phys. Lett. 31A, 273 (1970).

1965 (1)

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Adair, R.

R. Adair, L. L. Chase, S. A. Payne, Phys. Rev. B 39, 3337 (1989).
[CrossRef]

Bae, Y.

Y. Bae, J. J. Song, Y. B. Kim, J. Appl. Phys. 53, 615 (1982).
[CrossRef]

Bepko, S. J.

S. J. Bepko, Phys. Rev. B 12, 669 (1975).
[CrossRef]

Bloembergen, N.

E. Yablonovitch, C. Flytzanis, N. Bloembergen, Phys. Rev. Lett. 29, 865 (1972).
[CrossRef]

Borshch, A. A.

A. A. Borshch, M. S. Brodin, V. N. Semioshko, Phys. Status Solidi A 91, 135 (1985).
[CrossRef]

Brodin, M. S.

A. A. Borshch, M. S. Brodin, V. N. Semioshko, Phys. Status Solidi A 91, 135 (1985).
[CrossRef]

Butcher, P. N.

P. N. Butcher, D. Cotter, Elements of Nonlinear Optics (Cambridge U. Press, London, 1990), Chap. 2.
[CrossRef]

Byer, R. L.

Canto-Said, E. J.

E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

Chase, L. L.

R. Adair, L. L. Chase, S. A. Payne, Phys. Rev. B 39, 3337 (1989).
[CrossRef]

Cotter, D.

P. N. Butcher, D. Cotter, Elements of Nonlinear Optics (Cambridge U. Press, London, 1990), Chap. 2.
[CrossRef]

DeSalvo, J. R.

J. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, E. W. Van Stryland, in Optical Society of America Annual Meeting Technical Digest (Optical Society of America, Washington, D.C., 1990), paper MTT7.

DeSalvo, R.

Echardt, R. C.

Fan, Y. X.

Feigelson, R. S.

Flytzanis, C.

E. Yablonovitch, C. Flytzanis, N. Bloembergen, Phys. Rev. Lett. 29, 865 (1972).
[CrossRef]

C. Flytzanis, Phys. Lett. 31A, 273 (1970).

Hagan, D. J.

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron 26, 760 (1990).
[CrossRef]

J. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, E. W. Van Stryland, in Optical Society of America Annual Meeting Technical Digest (Optical Society of America, Washington, D.C., 1990), paper MTT7.

Hu, B. Q.

Huang, C. E.

Hutchings, D. C.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

Kim, Y. B.

Y. Bae, J. J. Song, Y. B. Kim, J. Appl. Phys. 53, 615 (1982).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Owyoung, A.

A. Owyoung, IEEE J. Quantum Electron. QE-11, 1064 (1973).
[CrossRef]

Payne, S. A.

R. Adair, L. L. Chase, S. A. Payne, Phys. Rev. B 39, 3337 (1989).
[CrossRef]

Said, A. A.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron 26, 760 (1990).
[CrossRef]

Semioshko, V. N.

A. A. Borshch, M. S. Brodin, V. N. Semioshko, Phys. Status Solidi A 91, 135 (1985).
[CrossRef]

Shablaev, S. I.

S. I. Shablaev, Sov. Phys. JETP 70, 1105 (1990).

Sheik-Bahae, M.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron 26, 760 (1990).
[CrossRef]

J. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, E. W. Van Stryland, in Optical Society of America Annual Meeting Technical Digest (Optical Society of America, Washington, D.C., 1990), paper MTT7.

Soileau, M. J.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, in Fifteenth Annual Symposium on Optical Materials for High Power Lasers (National Bureau of Standards, Washington, D.C., 1983).

Song, J. J.

Y. Bae, J. J. Song, Y. B. Kim, J. Appl. Phys. 53, 615 (1982).
[CrossRef]

Stegeman, G. I.

Terhune, R. W.

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Van Stryland, E. W.

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron 26, 760 (1990).
[CrossRef]

J. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, E. W. Van Stryland, in Optical Society of America Annual Meeting Technical Digest (Optical Society of America, Washington, D.C., 1990), paper MTT7.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, in Fifteenth Annual Symposium on Optical Materials for High Power Lasers (National Bureau of Standards, Washington, D.C., 1983).

Vanherzeele, H.

Wang, J.

Wei, T. H.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron 26, 760 (1990).
[CrossRef]

Williams, W. E.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, in Fifteenth Annual Symposium on Optical Materials for High Power Lasers (National Bureau of Standards, Washington, D.C., 1983).

Yablonovitch, E.

E. Yablonovitch, C. Flytzanis, N. Bloembergen, Phys. Rev. Lett. 29, 865 (1972).
[CrossRef]

Yee Fan, T.

Young, J.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, E. W. Van Stryland, J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron 26, 760 (1990).
[CrossRef]

IEEE J. Quantum Electron. (2)

E. J. Canto-Said, D. J. Hagan, J. Young, E. W. Van Stryland, IEEE J. Quantum Electron. 27, 2274 (1991).
[CrossRef]

A. Owyoung, IEEE J. Quantum Electron. QE-11, 1064 (1973).
[CrossRef]

J. Appl. Phys. (1)

Y. Bae, J. J. Song, Y. B. Kim, J. Appl. Phys. 53, 615 (1982).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, Opt. Quantum Electron. 24, 1 (1992).
[CrossRef]

Phys. Lett. (1)

C. Flytzanis, Phys. Lett. 31A, 273 (1970).

Phys. Rev. (1)

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Phys. Rev. B (2)

R. Adair, L. L. Chase, S. A. Payne, Phys. Rev. B 39, 3337 (1989).
[CrossRef]

S. J. Bepko, Phys. Rev. B 12, 669 (1975).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, C. Flytzanis, N. Bloembergen, Phys. Rev. Lett. 29, 865 (1972).
[CrossRef]

Phys. Status Solidi A (1)

A. A. Borshch, M. S. Brodin, V. N. Semioshko, Phys. Status Solidi A 91, 135 (1985).
[CrossRef]

Sov. Phys. JETP (1)

S. I. Shablaev, Sov. Phys. JETP 70, 1105 (1990).

Other (3)

P. N. Butcher, D. Cotter, Elements of Nonlinear Optics (Cambridge U. Press, London, 1990), Chap. 2.
[CrossRef]

W. E. Williams, M. J. Soileau, E. W. Van Stryland, in Fifteenth Annual Symposium on Optical Materials for High Power Lasers (National Bureau of Standards, Washington, D.C., 1983).

J. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, E. W. Van Stryland, in Optical Society of America Annual Meeting Technical Digest (Optical Society of America, Washington, D.C., 1990), paper MTT7.

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Figures (2)

Fig. 1
Fig. 1

Curve (a), 532-mn 40% aperture transmittance trace as a function of incident electric-field polarization in BaF2. Curve (b), 1064-nm trace in KTP to measure the polarization dependence of n2.

Fig. 2
Fig. 2

Curve (a), 532-nm data for KTP showing variation in change in transmittance as a function of incident polarization. Curve (b), 1064-nm trace in [110] GaAs showing variation in transmittance as a function of incident electric-field polarization.

Tables (1)

Tables Icon

Table 1 Summary of Nonlinear Coefficients n2 and β Measured at 532 and 1064 nm

Equations (9)

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I ( r , z , t ) z = α I ( r , z , t ) β I ( r , z , t ) 2 ,
P ( 3 ) ( ω ) = 3 o 4 χ eff ( 3 ) ( θ ) E o 3 ,
n 2 ( m 2 / W ) = 3 4 o c n o 2 Re χ ( 3 ) ( ω ; ω , ω , ω )
β ( m / W ) = 3 ω 2 o c 2 n o 2 Im χ ( 3 ) ( ω ; ω , ω , ω ) ,
χ eff ( 3 ) ( θ ) = χ x x x x ( 3 ) [ 1 + 2 σ ( sin 4 θ sin 2 θ ) ] ,
σ = χ x x x x ( 3 ) [ χ x x y y ( 3 ) + 2 χ x y y x ( 3 ) ] χ x x x x ( 3 ) .
χ eff ( 3 ) ( ϕ ) = χ x x x x ( 3 ) cos 4 ϕ + χ y y y y ( 3 ) sin 4 ϕ + B sin 2 2 ϕ 4 ,
B = 2 χ x x y y ( 3 ) + 2 χ y y x x ( 3 ) + χ x y y x ( 3 ) + χ y x x y ( 3 ) .
χ eff ( 3 ) ( θ ) = χ x x x x ( 3 ) [ 1 + 2 σ ( 3 4 sin 4 θ sin 2 θ ) ] .

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